Course: MATH-UA 125 Introduction to Mathematical Proofs/ MTHED-UE 1049 Mathematical Proof and Proving
Course Description: This course introduces elements of mathematical proof, focusing on three mains themes: 1. The meaning of mathematical statements -- universal/existential; 2. The role of examples in determining the validity of mathematical statements; 3. The various forms and methods of mathematical proofs, including direct (deductive) proof; proof by exhaustion; indirect proof (by contradiction, or by contrapositive); mathematical induction; and disproof by counterexample. This is a problem-based course. Lessons are structured around activities that engage students in doing proofs that are meaningful to them and based on mathematical topics with which they are familiar.
Instructors: Jalal Shatah and Orit Zaslavsky, shatah(at-sign)cims.nyu.edu, oz2(at-sign)nyu.edu
Meeting Time/Location: Monday 1145AM-2PM, (formerly KIMM 804) changed to WWH 317
TA: Steven Heilman, heilman(at-sign)cims.nyu.edu
TA Office Hours: WWH 1108, Thursday, 11AM-1PM, or by appointment
(If this time is bad for many people, let me know and I will make a change.)
Recommended Textbooks: Chartrand, Polimeni and Zhang, Mathematical Proofs: A Transition to Advanced Mathematics.
Fendel and Resek, Foundations of Higher Mathematics: Exploration and Proof.
Other Resources: An introduction to mathematical arguments, Michael Hutchings
An Introduction to Mathematical Proofs, Jimmy Arnold. ch1 ch2 ch3 ch4 ch5